Previous attempts to predict chromatic-adaptation correspondence have led to a sharpening dilemma-i.e., Von Kries primaries are chosen that do not include in the positive octant all the realizable (x,y) chromaticities. This leads to paradoxical adaptation predictions for the colors that have negative Von Kries coordinates. A solution is proposed here that expresses the asymmetric-matching relation of chromatic adaptation as the product of two matrix transformations, given source illuminant 1 and destination illuminant 2: from source tristimulus values via adaptation matrix 1 to the adapted state coordinates, and from the adapted state via the inverse of adaptation matrix 2 to the destination illuminant tristimulus values. To avoid the sharpening instability, the entire spectrum locus must lie within the positive octant of the adapted state tristimulus space.